Against Irrationalism and Particularism, or,
the Fake Issue of "Western Mathematics"

by Ralph Dumain

The science resulting from all human knowledge has no nationality. The ridiculous disputes about the origin of such and such a discovery do not interest us since they add nothing to the value of the discovery. It can therefore be said that African unity offers the world a new humanism essentially founded on the universal solidarity and co-operation between people without any racial and cultural antagonism and without narrow egoism and privilege.

--- Sekou Toure1

Alan J. Bishop's article "Western Mathematics: The Secret Weapon of Cultural Imperialism"2 reflects the cult of irrationalism and obscurantism that dominates the world today, an ethos that augurs a new dark night of fascism. The reactionary spirit of Bishop's article is a far cry from the universalist humanism prevalent in the era of anti-colonial revolt as expressed in the quote above.3

In keeping with its irrationalist spirit, Bishop conflates four distinct issues: (1) the nature of mathematics and truth, (2) systems of notation and measurement, (3) mathematics pedagogy, and (4) history and social origins of mathematics. Since he hates reason, he is hardly bothered by the contradictions in his argument. First comes his one moment of philosophical truth:

There is no doubt that mathematical truths like those [2 x 2 = 4, etc.] are universal. They are valid everywhere, because of their intentionally abstract and general nature.

Then he delves into questions of notation -- radial measurement, systems of counting, uses of symbols -- asserts that these have a cultural history, and denies the university of modern ("western") mathematics, thus contradicting his statement above. But cultural history and notational conventions have nothing whatever to do with the essence of mathematics or the nature of mathematical truths, whose abstraction and generality make them universal. Granted that mathematics has social origins and functions, but mathematics comes into its own precisely when it is conscious of itself as system, as abstraction. Any other stance is nihilistic anti-intellectualism, whose disastrous consequences are proved by the course of twentieth century history, i.e. in Nazism, Stalinism, and Maoism.

Bishop also contradicts himself in deliberating whether "mainstream" mathematics should even be called western. He decides to do so in spite of its multicultural character, reinforcing the very racism he purportedly seeks to combat.

Bishop links European notation and measurement and uses of mathematics to imperialist penetration and systems of administration. However interesting, this once again is absolutely irrelevant to the objective truth value of mathematics. It should not be surprising that a more evolved mode of production, scientific and technological knowledge, and division of labor would enable the transcendence of "finite and limited" counting systems, and good riddance to them too. Why be nostalgic over obsolete and limited conceptions? Bishop's attitude is suspiciously reminiscent of fascist Mobutu "authenticity", i.e. of a retrograde fraud.4

Bishop brings up an interesting and legitimate pedagogical and political issue, i.e. the cultural biases used in mathematical exercises in colonial Africa. Nevertheless, it has nothing to do with mathematics proper. In defending "pure" mathematics, by the way, I do not mean to suggest that mathematics is unconnected to the material world or irrelevant to practical activity, but there remains a vital distinction. Because it is human nature to work up to the abstract starting from concrete examples, being able to relate seemingly detached abstractions to the student's concrete experience, frame of reference, and practical needs is an obviously important issue for teaching, learning, and practice, but the ultimate goal is to attain a level of abstraction by which mathematics can be applied to any content. This is now recognized by virtually all Marxist philosophers of science, who are known to have a high respect for the concrete and being able to relating the abstract to it. Engels understood this too, unlike Stalin and Mao. If you don't understand this, you don't understand dialectics.

Then Bishop tips his hand by attacking the values associated with "western" mathematics: rationalism, "objectism", technological mastery of the physical environment. Horrible values, no? Bishop counterposes this apparently reprehensible value system to what Robin Horton, a stupid westerner who takes refuge in atavism to escape the modern world, thinks are the admirable qual- ities of Africans, i.e. being anti-intellectual, people-oriented, and thus indifferent to the world of things. Look at the virtues Horton finds in traditional societies:

In traditional cultures there is no developed awareness of alternatives to the established body of theoretical tenets; whereas in scientifically oriented cultures such an awareness is highly developed.

Bishop also goes along with Lancy, according to whom British culture mistakenly teaches children that the referential function of language is most important, while:

The Kaluhi child learns that the most important language functions are expressive; specifically, that the competent language user is one who can use speech to manipulate and control the behavior of others.

These are Bishop's precious traditional values: manipulation of people rather than things, provincialism and lack of self-criticism, unwillingness to evaluate and compare assertions about reality. God forbid, the western ethnocentric proclivity for logical reasoning is prejudiced against "mere trial and error practices, traditional wisdom and witchcraft", which are superior to "cold logic".

I would not deny that "ethno-mathematics" could be of value in improving mathematical instruction in different social environments, for the reasons mentioned above. And, although the teaching of mathematical competencies is a goal distinct from cultural appreciation and awareness, teaching the contributions of various civilizations to the development of mathematics could only be helpful to social progress, certainly to the project of combatting the mythology of white supremacy. However, the ultimate goal remains the ability to use the tools of modern mathematics, whose objective value renders any concern over the role of white males in it childish and pointless. Bishop shares the fallacious conceit of the philosophical relativist: just because knowledge is produced in a social context and expresses social interests, it cannot therefore be objectively valid as well. To undermine reason with religious and "spiritual" values is poison. For traditional societies to deliberately cling to this aspect of their culture condemns them to inferiority and obsolescence.

Bishop's opposition of abstraction and context reveals another dimension of his philosophical incompetence. To be context-bound is not to be able to think at all, to be an idiot. How is it possible to preserve a concept of the whole, i.e. the concrete, where everything relates to everything else, and yet to be able to abstract? This is an utter mystery to Bishop. And yet this problem, central to the nature of thought, demands a solution. To be able to abstract out of the particular context, and to be able to reproduce the concrete in thought by way of the abstract, is the method of Marx, of all science in fact, and it transcends Bishop's infantile anti-scientific contextualism.

It would be bigoted to deny the ability of human beings prior to the fifteenth century, European or not, to have been able to think. But conceptual as well as social revolutions occur in history. Readers of this article will already know something about the bourgeois revolution that created the material basis for the scientific revolution. On a conceptual level, we can adduce Albert Einstein's comment that the modern scientific spirit is a result of the development of the axiomatic method along with systematic empirical methods, which he considered a nearly miraculous achievement for anyone rather than an occasion for boasting about any putative superiority of Europeans. The development of these methods, the evolution of thought to ever greater levels of generality and abstraction, the axiomatization of mathematics, the creation of modern branches of mathematics such as calculus, probability theory, number theory, topology, mathematical logic and foundations, have created a conceptual apparatus superior to all prior knowledge on which it has been built. To deny objective progress, to deny these magnificent achievements to the third world would be criminal. Who stands to gain by keeping the masses ignorant? Why, manipulative petit bourgeois nationalists, of course.

Bishop's gambit is a familiar one. It is passive-aggressive pseudo-militancy: separatist boasting masking a cowardly capitulation to segregationism, a game played by various bourgeois nationalist intellectuals in the third world and especially by the fraudulent black nationalists here in the United States. It is an old trick of the power-hungry petit bourgeois who seeks to capitalize on ghettoization for his own profit. Bishop's penchant for superstition and incoherence reflects the typical alienation, cynicism, and decadence of the contemporary bourgeois intellectual. This outlook of Bishop and thousands like him can only hold third world peoples back. Such counterrevolutionary, racist and fascist ideological filth should not be allowed to pass without challenge.

1 Quoted in Raya Dunayevskaya, Nationalism, Communism, Marxist Humanism and the Afro-Asian Revolutions (Chicago: News & Letters, 1984), p. 32.

2 Race & Class (vol. 32, no. 2, October-December 1990), p. 51-65.

3 The reversion to "local" and "regional rationality" is approvingly documented in V.Y. Mudimbe, The Invention of Africa: Gnosis, Philosophy and the Order of Knowledge (Bloomington; Indianapolis: Indiana University Press, 1988).

4 For a healthy reaction to this nonsense see Paulin J. Hountondji, "Marxism and the Myth of an "African Ideology"", in Rethinking Marx, edited by Sakari Hanninen and Leena Paldan (New York; Bagnolet, France: International General/IMMRC, 1984), pp. 103-108.

(12 December 1991)

NOTE: This essay was refused for publication in Race and Class.

©1991, 2000 Ralph Dumain

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